Fiber optic microseismic sensing systems

ABSTRACT

A fiber optic microseismic sensing system is provided. The system includes a plurality of nodes, each of the nodes including a surface portion, an underground portion, and an optical cable extending between the surface portion and the underground portion. The surface portion includes (1) an optical source for transmitting an optical signal along the optical cable to the underground portion, and (2) an optical receiver for receiving a return optical signal propagating along the optical cable from the underground portion. The underground portion includes at least one transducer, each of the at least one transducer including (1) a fixed portion configured to be secured to a body of interest, (2) a moveable portion having a range of motion with respect to the fixed portion, (3) a spring positioned between the fixed portion and the moveable portion, and (4) a mass engaged with the moveable portion. The optical cable includes a length of fiber wound between the fixed portion and the moveable portion of each of the at least one transducer, the length of fiber spanning the spring. In one disclosed aspect of the transducer, the mass envelopes the moveable portion.

RELATED APPLICATION

This application claims the benefit of priority to U.S. Provisional Patent Application Ser. No. 61/279,607, filed on Oct. 23, 2009, the contents of which are incorporated in this application by reference.

TECHNICAL FIELD

This invention relates generally to the field of microseismic sensing, and more particularly, to improved fiber optic microseismic sensing systems.

BACKGROUND OF THE INVENTION

Certain movements of the earth may be referred to in the art as “microseisms,” “microseismic disturbances,” and/or “microseismic perturbations.” For example, earth tremors (e.g., tectonic plate motion) such as those caused by natural phenomena (e.g., wind, ocean waves, earthquakes, etc.) may be considered to be microseisms. Further, man-made earth perturbations (e.g., perturbations caused by hydrofracturing, steam injection, carbon sequestration, etc.) may also be considered to be microseisms.

The technology to sense microseisms using fiber optic sensing systems is known. Fiber optic sensing systems are widely used for sensing disturbances (e.g., motion, acceleration, sound, etc.). Such fiber optic sensing systems often include a transducer for converting the disturbance into a phase change of light in an optical fiber.

Prior art transducers used to sense microseisms suffer from a number of deficiencies. For example, certain fiber optic sensing applications have spatial restrictions which limit the applicability of certain transducer designs. Further, the environment in which the transducers (and other optical elements of the fiber optic sensing systems) are used may require sensitivity and control not obtained or available from many conventional transducers. Further still, the operation of many optical transducers is adversely affected by disturbances along differing axes of motion.

Thus, it would be desirable to provide improved fiber optic transducers, and fiber optic accelerometers, and related fiber optic microseismic sensing systems to address these and other issues.

BRIEF SUMMARY OF THE INVENTION

According to an exemplary embodiment of the present invention, a fiber optic microseismic sensing system is provided. The system includes a plurality of nodes, each of the nodes including a surface portion, an underground portion, and an optical cable extending between the surface portion and the underground portion. The surface portion includes (1) an optical source for transmitting an optical signal along the optical cable to the underground portion, and (2) an optical receiver for receiving a return optical signal propagating along the optical cable from the underground portion. The underground portion includes at least one transducer, each of the at least one transducer including (1) a fixed portion configured to be secured to a body of interest, (2) a moveable portion having a range of motion with respect to the fixed portion, (3) a spring positioned between the fixed portion and the moveable portion, and (4) a mass engaged with the moveable portion. The optical cable includes a length of fiber wound between the fixed portion and the moveable portion of each of the at least one transducer, the length of fiber spanning the spring.

The transducer may be included as part of an accelerometer. The transducer/accelerometer may include various additional features that are not mutually exclusive with respect to one another. For example, the mass may be configured to envelope the moveable portion (as well as other portions of the transducer). Further, the mass may house certain optical elements (e.g., a reflector, a fiber optic coupler, etc.) of the accelerometer. Further still, certain of the elements of the transducer (e.g., the fixed portion, the moveable portion, and the spring) may be formed from a unitary piece of material.

The plurality of nodes, or field nodes of the inventive fiber optic microseismic sensing systems may be Sagnac interferometer sensing systems, Michelsen interferometer sensing systems, and Fabry Perot interferometer sensing systems, amongst others.

It is to be understood that both the foregoing general description and the following detailed description are exemplary, but are not restrictive, of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention is best understood from the following detailed description when read in connection with the accompanying drawings. It is emphasized that, according to common practice, the various features of the drawings are not to scale. On the contrary, the dimensions of the various features are arbitrarily expanded or reduced for clarity purposes. Included in the drawings are the following figures:

FIG. 1 is a block diagram illustration of a fiber optic accelerometer in accordance with an exemplary embodiment of the present invention;

FIGS. 2A-2H are cross-sectional block diagram views of transducers in accordance with various exemplary embodiments of the present invention;

FIGS. 2I-2J are top and bottom perspective views of a transducer in accordance with an exemplary embodiment of the present invention;

FIG. 3A is a block diagram view of a linearized Sagnac interferometer in accordance with an exemplary embodiment of the present invention;

FIG. 3B-3C are block diagram views of Michelsen interferometers in accordance with various exemplary embodiments of the present invention;

FIG. 4A is a block diagram view of a plurality of multiplexed Sagnac interferometers in accordance with an exemplary embodiment of the present invention;

FIG. 4B is a block diagram view of a plurality of multiplexed Fabry Perot interferometers in accordance with an exemplary embodiment of the present invention;

FIG. 5 is an exploded view of a transducer in accordance with an exemplary embodiment of the present invention;

FIGS. 6A-6B are top and perspective views of a hinge of the transducer of FIG. 5;

FIG. 6C illustrates exemplary mounting of the hinge of FIGS. 6A-6B;

FIG. 7A is a sectional block diagram view of a transducer in accordance with an exemplary embodiment of the present invention;

FIGS. 7B-7C are block diagram views of damping modes of the transducer of FIG. 7A; and

FIG. 8 is a block diagram view of a fiber optic microseismic sensing system in accordance with an exemplary embodiment of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

According to various exemplary embodiments of the present invention, fiber optic microseismic sensing systems are provided. For example, the sensing systems may include an array of fiber optic sensors (also known as fiber optic accelerometers or fiber optic interferometers) for sensing underground perturbations within a volume of the earth. For example, the array may be a three dimensional array of fiber optic sensors. Each of the sensors includes one or more fiber optic transducers (e.g., three transducers could be used for sensing disturbances in three directions). The sensors may be arranged to sense the underground perturbations/disturbances in a plurality of dimensions, and at a plurality of depths, for mapping the perturbations in the volume. The sensing systems may operate continuously if desired (or may be operated at a given time, or at predetermined time intervals, etc.) in order to continuously generate data that can be processed for generating sub-surface maps that identify the source of the disturbance(s) over time.

FIG. 8 illustrates an exemplary fiber optic microseismic sensing system including a plurality of field nodes for sensing perturbations in underground volume 816. For example, a first field node (surrounded by the dotted line enclosure on the left side of FIG. 8) includes underground portion 802 a, surface portion 804 a, and optical cable 806 a extending between underground portion 802 a and surface portion 804 a. A second field node includes underground portion 802 b, surface portion 804 b, and optical cable 806 b; and a third field node includes underground portion 802 c, surface portion 804 c, and optical cable 806 c. Any of a number of additional field nodes may be included in the fiber optic microseismic sensing system as indicated by the nth field node including underground portion 802 n, surface portion 804 n, and optical cable 806 n.

Each of underground portions 802 a, 802 b, 802 c, 802 n includes at least one fiber optic transducer. The at least one fiber optic transducer may be, for example, any of the transducers described herein. For example, the at least one transducer may include (1) a fixed portion configured to be secured to a body of interest, (2) a moveable portion having a range of motion with respect to the fixed portion, (3) a spring positioned between the fixed portion and the moveable portion, and a (4) mass engaged with the moveable portion. These and other elements of the underground portion (e.g., optical elements of a fiber optic interferometer as will be described below) may be housed within an underground enclosure (e.g., an underground pod which can act as the body of interest to which the fixed portion of the transducer is secured). As will be appreciated by those skilled in the art, a single underground portion may include a transducer(s) at a plurality of underground depths (e.g., where the transducer(s) may be housed within an underground enclosure at each depth). Further, at each sensing location (e.g., within an underground enclosure at a given depth) there may be a plurality of transducers arranged to sense disturbances in differing directions. For example, at a given sensing location, one transducer may be configured to sense a disturbance along the x-axis, another transducer may be configured to sense a disturbance along the y-axis, and yet another transducer may be configured to sense a disturbance along the vertical z-axis, where x-axis, y-axis and z-axis refer to a set of three orthogonal directions in space.

Each of surface portions 804 a, 804 b, 804 c, 804 n includes (1) an optical source for transmitting an optical signal along the optical cable 806 a, 806 b, 806 c, 806 n to a corresponding underground portion, and (2) an optical receiver for receiving a return optical signal propagating along the optical fiber from the corresponding underground portion. That is, each of surface portions 804 a, 804 b, 804 c, 804 n includes optical/electronics elements to interrogate the sensors below in the respective underground portion by providing optical illumination using the optical source via the respective optical cable 806 a, 806 b, 806 c, 806 n; and to interrogate the return optical signals using the optical receiver (and if desired, a phase demodulator). Of course, each of surface portions 804 a, 804 b, 804 c, 804 n may include additional elements such as additional optical elements, electronics, data storage, data processing equipment (e.g., a processor for operating on the received data through filtering, decimation, etc.), power generation and storage equipment, communications equipment (e.g., one or more wired and/or wireless communications transceivers), etc. In a specific example, each surface portion 804 a, 804 b, 804 c, 804 n may include one or more solar cells for generating power for use within the field node, and batteries or other power storage elements for providing back-up or uninterruptible power for use within the field node (where such batteries may be charged using the solar cell generated power and a charging circuit).

Each of optical cables 806 a, 806 b, 806 c, 806 n extend between their respective underground portion and surface portion. Each optical cable 806 a, 806 b, 806 c, 806 n may include a single active optical fiber, or a plurality of optical fibers. As will be appreciated by those skilled in the art, in an embodiment where multiple transducers are provided at a given sensing location (e.g., at a given depth, in a given underground sensing pod, etc.), a single optical fiber may be used to sense disturbances at each transducer. Further, in an embodiment where a given field node includes sensing locations at a plurality of depths (where each sensing location may include a plurality of transducers), a single optical fiber may be used to sense disturbances at each depth (and within all of the transducers at each depth). Of course, separate optical fibers may be used for sensing at each sensing location, or within each transducer at a single sensing location.

The fiber optic microseismic sensing system shown in FIG. 8 also includes remote node 812. Remote node 812 receives data from each of the field nodes (e.g., through wired connection 810, through wireless communication transceivers 814, 808 a, 808 b, 808 c, 808 n, etc.), and converts the received data into microseismic image data (e.g., mapping of the underground volume). That is, remote node 812 contains data storage (e.g., digital data storage), and may contain data processing equipment for mapping the underground volume using the sensed seismic activity (e.g., three dimensional mapping of the underground volume). Alternatively, an additional node (e.g., a further remote node, an intermediate node, etc.) in communication with the remote node (and/or the field nodes) may be used to perform the mapping of the underground volume. The remote node itself may include one or more transducers at one or more depths along one or more optical cables (i.e., the remote node may function as one of the field nodes, as well as having the function of the remote node).

FIG. 8 illustrates a depth “d” that the underground portion is below the ground level. Of course, depth “d” may vary widely, especially in applications where each field node includes sensing locations at a plurality of depths. An exemplary range for depth “d” may be a depth greater than approximately 100 feet, and another exemplary range for depth “d” is between 100 to 1000 feet. FIG. 8 also illustrates spacing “sp” between adjacent field nodes. An exemplary range for spacing “sp” is between 20-100 feet. Of course, while FIG. 8 illustrates a plurality of field nodes arranged in a linear arrangement, it is clear that the nodes may extend in various different directions (e.g., in a direction perpendicular to the line of field nodes shown in FIG. 8). In a particular example, field nodes may be arranged in a grid configuration (e.g., rows and columns of field nodes).

The inventive fiber optic microseismic sensing systems make use of transducers (and accelerometers, interferometers, sensors using such transducers) for sensing physical disturbances (e.g., motion, acceleration, perturbations, etc.) of a body of interest. As will be appreciated by those skilled in the art, a fiber optic accelerometer (sometimes referred to as a fiber optic sensor or a fiber optic interferometer) is an element of a system for measuring physical motion of a body of interest using fiber optic technology. The accelerometer includes a transducer that converts a physical disturbance of the body of interest into a change in strain applied to a length of optical fiber of the transducer.

Referring to FIG. 1, fiber optic accelerometer 10 includes optical source 20 (e.g., an LED, an SLED, a laser, etc.), sensor 30 (e.g., an interferometer), optical receiver 60 (e.g., an optical detector such as a photodetector), optical fiber 40 for transmitting light from optical source 20 to sensor 30, and optical fiber 50 for returning light from sensor 30 to receiver 60. Sensor 30 includes a transducer which converts mechanical or physical motion (such as acceleration) to a change in the strain (e.g., longitudinal strain) in an optical fiber. Sensor 30 also includes other optical elements for converting the change in strain to a change in the phase of light that passes through the optical fiber 40, 50. FIGS. 2A-2H illustrate various transducers which may be included in sensor 30 of FIG. 1.

FIG. 2A illustrates transducer 200 including fixed portion/mandrel 205 and moveable portion/mandrel 210 separated by spring 230. Optical fiber 150 (illustrated as a dashed box between mandrels 205, 210) is wound around fixed mandrel 200 and moveable mandrel 210, where spring 230 applies a biasing tension to optical fiber 150 (e.g., with an example tension of the wound length of optical fiber 150 being approximately between 0.1-4.0 newtons). Optical fiber 150 may be fixed to mandrels 205, 210 at the ends of the wound portion using an adhesive (not shown) if desired (e.g., epoxy, acrylate adhesive, etc.). Mass 220 is secured to moveable mandrel 210 (e.g., using fasteners such as screws, using a rigid adhesive, etc.). Alternatively, mass 220 and moveable mandrel 210 may be formed from a unitary piece of material. Example materials of mandrels 205, 210 (and mass 220) are metals (e.g., aluminum, stainless steel, brass, etc.) and plastics (e.g., polycarbonate). Hinges 240 a, 240 b (which are provided between fixed mandrel 205 and mass 220) limit the range of motion of moveable mandrel 210 (and mass 220) to a direction substantially along axis labeled as axis “Y”, where axis “Y” is a single linear degree of freedom that is substantially parallel to interior wall portion 220 w of enveloping mass 220 (and is substantially parallel to an imaginary line connecting mandrels 205 and 210). The exemplary hinges 240 a, 240 b shown in the cross-sectional view of FIG. 2A are circular hinges similar in function to hinge 210 n described below with respect to FIG. 5.

Fixed mandrel 205 is rigidly attached to body of interest 202, or may be rigidly attached to body of interest 202 through a base plate or other structure (not shown). When body of interest 202 undergoes acceleration (or other physical disturbance) in space, the result is relative motion between fixed mandrel 205 and moveable mandrel 210/mass 220. This relative motion changes the longitudinal strain within optical fiber 150. As provided above, this change in the longitudinal strain in optical fiber 150 is converted to a change in the phase of light as the light passes through optical fiber 150.

In transducer 200 shown FIG. 2A (and in various other exemplary transducers such as those shown in FIGS. 2B-2E and FIGS. 2G-2H), mass 220 envelopes at least one of fixed mandrel 205, spring 230, and/or the wound length of fiber 150 within at least one position (or within every position) within the range of motion of moveable portion 210. That is, mass 220 has a substantially cylindrical shape where inner side walls 220 w of the cylindrical shape surround (i.e., envelope) at least one of fixed mandrel 205, spring 230, and/or the wound length of fiber 150. By enveloping such elements with mass 220, various benefits are provided. For example, the mass provided per volume of the transducer is relatively high because of the enveloping shape of mass 220. Further, the enveloping shape assists in controlling the center of gravity of the mass 220. Further still, the enveloping shape of the mass 220 reduces sensitivity to off-axis excitation. The features and details described above with respect to FIG. 2A are applicable to the exemplary embodiments shown in FIGS. 2B-2H unless indicated otherwise.

FIG. 2B illustrates transducer 200 a including fixed mandrel 205 a, moveable mandrel 210 a, and spring 230 a separating mandrels 205 a, 210 a. Optical fiber 150 a is wound around fixed mandrel 205 a and the moveable mandrel 210 a. Mass 220 a is secured to moveable mandrel 210 a, or alternatively, mass 220 a, and moveable mandrel 210 a may be formed from a unitary piece of material. Fixed mandrel 205 a is rigidly attached to body of interest 202 a, or may be rigidly attached to body of interest 202 a through a base plate or the like. When body of interest 202 a undergoes acceleration (or another physical disturbance) in space, the result is relative motion between fixed mandrel 205 a and moveable mandrel 210 a/mass 220 a. This relative motion changes the longitudinal strain within optical fiber 150 a, where such longitudinal strain in optical fiber 150 a is converted to a change in the phase of light as the light passes through optical fiber 150 a. FIG. 2B differs from FIG. 2A primarily in terms of the shape of certain of the elements; however, the function of the elements is substantially the same.

FIG. 2C is substantially similar to FIG. 2B, except that the elements illustrated have reference numerals ending with “b” instead of “a”. The primary difference between FIG. 2C and FIG. 2B is that in FIG. 2C spring 230 b is a bent sheet metal spring (as opposed to the coil compression style spring shown in FIG. 2B) that can also provide a hinge function, similar to hinges 240 a, 240 b described above with respect to FIG. 2A, as well as a biasing spring function. Of course, other types of spring members are contemplated.

As will be appreciated by those skilled in the art, the mass does not need to be a cylindrical enveloping mass as shown in FIGS. 2A-2C, that is, other shapes are contemplated. FIGS. 2D-2E are substantially similar to FIG. 2B, except that the elements illustrated have reference numerals ending with “c”/“d” instead of “a”; however, the shapes of the enveloping mass 220 c and 220 d is varied in FIGS. 2D-2E. In FIG. 2D, enveloping mass 220 c has a biconical shape (as opposed to a cylindrical shape as in FIG. 2B). In FIG. 2E, enveloping mass 220 d has a spherical shape. As with mass 220 (described above in connection with FIG. 2A), mass 220 c/220 d envelopes other portions of the transducer within the range of motion (or at least one position within the range of motion) of the moveable portion of the transducer, as desired. Other exemplary shapes of the enveloping mass include a conical shape, a rhombic shape, amongst others.

As will be appreciated by those skilled in the art, each of the transducers illustrated in FIGS. 2A-2H may be included in an optical interferometer (also referred to as a “sensor”). Such an optical interferometer includes optical elements that perform functions including the conversion of the change in the phase of light passing through the fiber in the transducer to a change in optical intensity. According to certain exemplary embodiments of the present invention, certain of these optical elements may be provided within the mass secured to (or integrated with) the moveable mandrel. FIG. 2F is substantially similar to FIG. 2B, except that the elements illustrated have reference numerals ending with “e” instead of “a”, and that the mass 220 e has a different shape (and an additional function) as compared to mass 220 a. Mass 220 e extends above moveable mandrel 210 e at a terminal end of the transducer (and in certain embodiments, a terminal end of the accelerometer). Mass 220 e defines a volume configured to house at least one optical element of the accelerometer. Exemplary optical elements that may be housed within mass 220 e include a fiber optic coupler, a reflector, an optical source (e.g., a light source), an optical receiver/detector, an optical depolarizer, a delay coil of optical cable, and a phase modulator. Any portion of these elements, and/or additional elements, may be housed within mass 220 e as is desired in the given application. Of course, the shape of mass 220 e illustrated in FIG. 2F is exemplary in nature—other shapes are contemplated. Further, while mass 220 e is not illustrated as an “enveloping” mass as described above, the present application contemplates a mass combining the features of housing optical elements as well as including the enveloping feature described above.

FIG. 2G illustrates transducer 200 f where each of fixed mandrel 205 f, spring 230 f, and moveable mandrel 210 f are formed from a unitary piece of material. Enveloping mass 220 f may be secured to moveable mandrel 210 f, or mass 220 f may be included in the unitary piece of material with moveable mandrel 210 f. As with the previously described embodiments, fixed mandrel 205 f is rigidly attached to body of interest 202 f, or may be rigidly attached to body of interest 202 f through a base plate or the like. A length of optical fiber 150 f is wound around fixed mandrel 205 f and the moveable mandrel 210 f. Otherwise, the function of transducer 200 f is substantially similar to that described above with respect to FIG. 2A.

FIG. 2H is substantially similar to FIG. 2B, except that the elements illustrated have reference numerals ending with “g” instead of “a”. The primary difference between FIG. 2H and FIG. 2B is that in FIG. 2H the spring function is provided by compressive bellows element 230 g. Element 230 g may have a hollow circular cross section, and may be defined by one or more metallic sub-elements, arranged to provide a spring function, but also creating lateral (and/or) torsional stiffness, as is well known by those skilled in the art.

FIGS. 2I-2J are top and bottom perspective views of a transducer such as that shown in FIGS. 2A-2H, excluding obvious distinctions such as the shape of the enveloping mass 220. Each of FIGS. 2A-2H includes a length of optical fiber (e.g., length of fiber 150, 150 a, 150 b, etc.) wound between the fixed mandrel and the moveable mandrel; however, none of FIGS. 2A-2H illustrates the fiber entering (or exiting) the transducer. That is, in FIGS. 2A-2H only that portion of the fiber wound between the fixed mandrel and the moveable mandrel is shown. FIGS. 2I-2J illustrate fiber 150 n entering (and exiting) transducer 200 n. Transducer 200 n includes top plate 204 n secured to enveloping mass 220 n and the moveable mandrel. Top plate 204 n is also secured to a moveable mandrel (not visible in FIGS. 2I-2J). Transducer 200 n also includes mounting plate 206 n, bottom plate 208 n (e.g., a retaining ring), and circular hinge 210 n. Bottom plate 208 n is used to secure circular hinge 210 n to mass 220 n. Mounting plate 206 n secures the inner region of circular hinge 210 n to a fixed mandrel (not visible in FIGS. 2I-2J). Mounting plate 206 n may also be used to secure transducer 200 n to a body of interest (or to an interposing structure) through mounting holes 212 n. Additional features of transducer 200 n will be described below in connection with the exploded view provided in FIG. 5.

As provided above, a transducer may be included as part of an interferometer, where the interferometer converts a change in the optical phase of light propagating along the optical fiber 150 within the transducer to a change in the optical intensity of the light leaving the interferometer. Transducers according to the present invention may be utilized in connection with any of a number of types of sensors/interferometers, and may be used in any of a number of varied applications. Exemplary sensors/applications for the transducers include fiber optic sensing systems. Exemplary fiber optic sensing systems include Sagnac interferometer sensing systems, Michelsen interferometer sensing systems, Fabry Perot interferometer sensing systems, and Mach-Zender interferometer sensing systems. FIG. 3A illustrates a linearized Sagnac sensing system including a single sensor, where such a Sagnac interferometer may be desirable because of a relatively small size and low cost. FIGS. 3B-3C illustrate Michelsen sensing systems, each including a single sensor. FIG. 4A illustrates a multiplexed Sagnac sensing system including a plurality of sensors. FIG. 4B illustrates a multiplexed Fabry Perot sensing system including a plurality of sensors.

Referring specifically to FIG. 3A, a fiber optic sensing system includes interferometer 300 (i.e., sensor 300, which is a linearized Sagnac interferometer) as well as optical source 302 and optical receiver 304. Interferometer 300 includes optical coupler 310 (e.g., a 3×3 optical coupler) for receiving an optical signal (e.g., light) from optical source 302, and for transmitting the optical signal out of interferometer 300 to optical receiver 304. First output lead 310 a of optical coupler 310 is connected to input lead 320 a of delay coil 320. Output lead 320 b of delay coil 320 is connected to first input lead 330 a of optical coupler 330 (e.g., a 1×2 fiber optic coupler 330). Second output lead 310 b of optical coupler 310 is connected to input lead 340 a of depolarizer 340. The third input lead of optical coupler 310 is not shown (as its end is tied off and/or crushed to minimize light that is reflected back into optical coupler 310). Depolarizer 340 significantly reduces polarization-induced signal fading allowing inexpensive single mode fiber to be used for all of the optical components and cable fibers rather than costly polarization-maintaining fiber. Depolarizer 340 may be one of several commercially available depolarizers, such as, for example, a recirculating coupler (single or multiple stage) or a Lyot Depolarizer. Output lead 340 b of depolarizer 340 is connected to input lead 330 b of optical coupler 330. First output lead 330 c of optical coupler 330 enters into transducer 200 (e.g., which may be any of the transducers illustrated or described within the present application) through optical fiber 150. Optical fiber 150 is wrapped (e.g., a desired number of turns) between the fixed mandrel and the moveable mandrel (described above), and the distal end of optical fiber 150 terminates at reflector 350 (e.g., broadband reflector 350). As will be appreciated by those skilled in the art, physical disturbances of the body of interest cause small changes in the length of fiber 150. These changes cause non-reciprocal changes in the phase of the light travelling through the Sagnac interferometer, and the interferometer converts the phase change of the light into an intensity change by allowing coherent interference between the light traveling in two counterpropagating directions, recombining at the optical coupler 330. This intensity change in the light is transmitted to optical receiver 304, where such intensity change is interpreted as motion/acceleration/disturbance of the body of interest by processor 306 connected to optical receiver 304.

FIGS. 3B-3C illustrate Michelsen interferometer fiber optic sensing systems 352, 380. System 352 illustrated in FIG. 3B includes internal modulation at sensor 352 a, while system 380 illustrated at FIG. 3B includes external modulation (i.e., external of sensor 380 a).

Referring specifically to FIG. 3B, optical source 354 (e.g., a laser) transmits an optical signal (e.g., laser light) to optical circulator 356. As will be appreciated by those skilled in the art, optical circulator 356 allows optical signals to pass only from port 1 to port 2, and from port 2 to port 3. The optical signal generated from laser 354 follows from port 1 to port 2, and along fiber length 360 within lead cable 358. Upon exiting optical coupler 362 (e.g., a 1×2 optical coupler) the optical signal is split between transducer 200 (e.g., which may be any of the transducers illustrated or described within the present application) and phase modulator 376. As will be appreciated by those skilled in the art, phase modulator 376 may include a reference coil. The split optical signals pass through the fiber within transducer 200 (including wound fiber length 150) and pass through phase modulator 376 and then reflect at reflectors 364, 366. Reflectors may be, for example, Faraday rotator mirrors. The reflected optical signals recombine (coherently) at optical coupler 362 and transmit back along fiber 360 within lead cable 358 to port 2 of optical circulator 356. From port 2 the recombined signal follows to port 3 of optical circulator 356, and then to optical receiver 368 (e.g., a photodetector or other optical detector). This recombined signal (which has a change in optical intensity which can be correlated to a disturbance of a body of interest) is converted at optical receiver 368 to electron hole pairs received by phase demodulator 370. Phase demodulator communicates with processor 372 for determination of the desired information related to the physical disturbance of the body of interest. As will be appreciated by those skilled in the art, phase demodulator 370 may generate a phase modulation drive signal (e.g., a carrier voltage drive signal) along wire 374 to phase modulator 376. That is, the power to control phase modulator 376 is carried along wire 374 (e.g., twisted copper wires 374).

FIG. 3C illustrates optical source 382 (e.g., a laser) that transmits an optical signal (e.g., laser light) to external phase modulator 384. The optical signal exiting phase modulator enters port 1 of optical circulator 386 and exits through port 2. From port 2 the optical signal enters optical coupler 388 of sensor 380 a where the optical signal is split. That is, the optical signal is split between transducer 200 (e.g., which may be any of the transducers illustrated or described within the present application) and reference coil 378. The split optical signals pass through the fiber within transducer 200 (including wound fiber length 150) and through reference coil 378 and then the optical signals reflect at reflectors 390, 398. Reflectors 390, 398 may be, for example, Faraday rotator mirrors. The reflected optical signals recombine coherently at optical coupler 388 and transmit back along fiber optic cable to port 2 of optical circulator 386. From port 2 the recombined signal follows to port 3 of optical circulator 386, and then to optical receiver 396 (e.g., a photodetector or other optical detector). This recombined signal (which has a change in optical intensity which can be correlated to a disturbance of a body of interest) is converted at optical receiver 396 to electron hole pairs received by phase demodulator 392. Phase demodulator communicates with processor 394 for determination of the desired information related to the disturbance of the body of interest. As will be appreciated by those skilled in the art, phase demodulator may generate a phase modulation drive signal (e.g., a carrier voltage drive signal) along wire 392 a (e.g., a twisted copper wire) to phase modulator 384.

As provided above, each of the exemplary fiber optic sensing systems of FIGS. 3A-3C includes a single sensor. Of course, it is often desirable to have fiber optic sensing systems with multiple sensors, for example, for sensing disturbances within a large area (and/or along a relatively long length). For example, as provided above with respect to FIG. 8, it may be desirable that a given field node have transducers (or groups of transducers) arranged at a plurality of depths. FIGS. 4A-4B illustrate fiber optic sensing systems including a plurality of sensors.

Referring specifically to FIG. 4A, a plurality of linearized Sagnac interferometers (e.g., interferometer 300 from FIG. 3A) are included in fiber optic sensing system 400. System 400 includes optical source 20, and optical receiver 60. Optical source 20 generates an optical signal in a pulsed mode with optical couplers 402 (e.g., 1×2 tap couplers 402) upstream of each interferometer 300, through optical circulator 404, to allow time division multiplexed operation, wherein return pulses from each interferometer 300 are received at optical receiver 60 at a different time. That is, tap couplers 402 are used to split the optical signal (e.g., the source light intensity) among several interferometers/sensors. The optical signal is pulsed, and return signals from each interferometer 300 return to optical receiver 60 at different times, but in their respective order of location. The return signals include intensity information proportional to the disturbance measured by each interferometer 300, where the information is processed by processor 406.

FIG. 4B illustrates fiber optic sensing system 408 including TDM (time division multiplexing) interrogator 410 for generating an optical signal. In this exemplary configuration, FBGs (i.e., fiber bragg gratings) are provided on each side of each transducer 200. Each transducer, and its surrounding FBGS, may be considered an interferometer 414 a, 414 b, etc. Each of FBGs 412 a, 412 b, 412 c, etc. act as partial reflectors. Interrogator 410 (which typically includes an optical source, a phase modulator, a light pulser, an optical receiver, and a phase demodulator) initiates an optical signal pulse that is partially reflected by each FBG 412 a, 412 b, 412 c, etc. Light reflected at pairs of each FBG 412 a, 412 b, 412 c, etc. is combined coherently. The combined signals arrive in time order such that TDM interrogator 410 (in connection with processor 416) can determine the light intensity change that results from the disturbance at each transducer 200.

FIG. 5 is an exploded view of transducer 200 n (previously described in connection with FIGS. 2I-2J). FIG. 5 illustrates fiber 150 n entering (and exiting) transducer 200 n at the same point adjacent to top plate 204 n. Top plate 204 n is secured to enveloping mass 220 n. Fiber 150 n is wound between moveable mandrel 210 n and fixed mandrel 205 n. Top plate 204 n is secured to moveable mandrel 210 n, and as such, enveloping mass 220 n is also secured to moveable mandrel 210 n through top plate 204 n. Biasing spring 230 n is disposed between fixed mandrel 205 n and moveable mandrel 210 n. Bottom plate 208 n secures circular hinge 210 n to mass 220 n. Mounting plate 206 n secures the inner region of circular hinge 210 n to fixed mandrel 205 n. As provided above, mounting plate 206 n may also be used to secure transducer 200 n to a body of interest (or to an interposing structure, not shown).

Circular hinge 210 n limits movement between objects attached to its inner diameter (in FIG. 5, fixed mandrel 205 n is configured to be attached to the inner diameter of hinge 210 n) and its outer diameter (in FIG. 5, mass 220 n is configured to be attached to the outer diameter of hinge 210 n). More specifically, circular hinge 210 n substantially limits relative motion between mass 220 n (secured to circular hinge 210 n) and fixed mandrel 205 n to substantially linear motion. Such linear motion may be along the “Y” axis described above with respect to FIGS. 2A-2H. FIGS. 6A-6B illustrate inner diameter 210 n 1 and outer diameter 210 n 2 of circular hinge 210 n. FIG. 6C illustrates inner diameter 210 n 1 secured to Structure #1, and outer diameter 210 n 2 secured to Structure #2.

In certain transducers according to the present invention, it may be desirable to provide for “damping” such as elastomeric damping, fluid damping, etc. That is, it is often desirable to reduce the quality factor of a transducer resonance peak by absorbing energy in the form of heat. Damping may also be used to increase the sensitivity of a transducer below its resonant frequency. FIG. 7A illustrates transducer 200 m (similar in most respects to transducer 200 a in FIG. 2B, except that the reference letter “a” has been replaced with reference letter “m”). A difference in transducer 200 m is the inclusion of elastomeric shear damping elements 224 and elastomeric compression damping elements 226. As shown in FIG. 7A, damping elements 224 are disposed between fixed mandrel 205 m and mass 220 m. Further, damping elements 226 are provided between mass 220 m and body of interest 202 m. FIG. 7B conceptually illustrates shear damping between mass 220 m and fixed mandrel 205 m, while FIG. 7C conceptually illustrates compression damping between mass 220 m and body of interest 202 m. Such damping techniques may be applied to each of the transducers illustrated and described in the present application.

Although the present invention is described primarily with respect to fiber optic microseismic sensing systems, it is not limited thereto. Additional exemplary applications for the transducers, accelerometers, and fiber optic sensing systems of the present invention include vertical seismic profiling (VSP), machine vibration monitoring, civil structure (e.g., dams, bridges, levees, buildings, etc.) monitoring, tunnel detection, perimeter/border security, earthquake monitoring, borehole leak detection, roadbed erosion, railbed erosion, amongst others.

Although various exemplary transducers of the present invention are described in connection with a fixed mandrel rigidly attached to a body of interest (or rigidly attached to the body of interest through a base plate or other structure) it is not limited thereto. For example, rather than such a rigid attachment, the fixed portion may be magnetized (or include a magnetized portion) such that the fixed portion may be secured to the body of interest, where the body of interest includes a ferrous material.

Although illustrated and described above with reference to certain specific embodiments, the present invention is nevertheless not intended to be limited to the details shown. Rather, various modifications may be made in the details within the scope and range of equivalents of the claims and without departing from the spirit of the invention. 

What is claimed:
 1. A fiber optic microseismic sensing system comprising: a plurality of nodes, each of the nodes including a surface portion, an underground portion, and an optical cable extending between the surface portion and the underground portion, the surface portion including (1) an optical source for transmitting an optical signal along the optical cable to the underground portion, and (2) an optical receiver for receiving a return optical signal propagating along the optical cable from the underground portion, the underground portion including at least one transducer, each of the at least one transducer including (1) a fixed portion configured to be secured to a body of interest, (2) a moveable portion having a range of motion with respect to the fixed portion, (3) a spring positioned between the fixed portion and the moveable portion, and (4) a mass engaged with the moveable portion, the mass enveloping the moveable portion, and the optical cable including a length of fiber wound between the fixed portion and the moveable portion of each of the at least one transducer, the length of fiber spanning the spring.
 2. The fiber optic microseismic sensing system of claim 1 wherein the underground portion includes an optical element for dividing the optical signal generated by the optical source, and for coherently recombining optical signals received by the optical element into the return optical signal.
 3. The fiber optic microseismic sensing system of claim 2 wherein the optical element is an optical coupler.
 4. The fiber optic microseismic sensing system of claim 1 wherein each of the field nodes of the microseismic fiber optic sensing system is a Sagnac interferometer sensing system.
 5. The fiber optic microseismic sensing system of claim 1 wherein each of the field nodes of the microseismic fiber optic sensing system is a Michelsen interferometer sensing system.
 6. The fiber optic microseismic sensing system of claim 1 wherein each of the field nodes of the microseismic fiber optic sensing system is a Fabry Perot interferometer sensing system.
 7. The fiber optic microseismic sensing system of claim 1 wherein the mass envelopes at least one of the fixed portion, the spring, and the length of fiber within at least one position within the range of motion of the moveable portion.
 8. The fiber optic microseismic sensing system of claim 1 wherein the mass envelopes the fixed portion within at least one position within the range of motion of the moveable portion.
 9. The fiber optic microseismic sensing system of claim 1 wherein the mass envelopes the spring within at least one position within the range of motion of the moveable portion.
 10. The fiber optic microseismic sensing system of claim 1 wherein the mass envelopes the length of fiber within at least one position within the range of motion of the moveable portion.
 11. The fiber optic microseismic sensing system of claim 1 wherein the mass envelopes each of the fixed portion, the spring, and the length of fiber within at least one position within the range of motion of the moveable portion.
 12. The fiber optic microseismic sensing system of claim 1 wherein the mass envelopes at least one of the fixed portion, the spring, and the length of fiber within the entire range of motion of the moveable portion.
 13. The fiber optic microseismic sensing system of claim 1 wherein the mass envelopes the fixed portion within the entire range of motion of the moveable portion.
 14. The fiber optic microseismic sensing system of claim 1 wherein the mass envelopes the spring within at least one position within the entire range of motion of the moveable portion.
 15. The fiber optic microseismic sensing system of claim 1 wherein the mass envelopes the length of fiber within at least one position within the entire range of motion of the moveable portion.
 16. The fiber optic microseismic sensing system of claim 1 wherein the mass envelopes each of the fixed portion, the spring, and the length of fiber within the entire range of motion of the moveable portion.
 17. The fiber optic microseismic sensing system of claim 1 wherein the spring is a biasing spring for providing tension to the length of fiber.
 18. The fiber optic microseismic sensing system of claim 1 further comprising a hinge connected between the mass and the fixed portion to limit the range of motion of the moveable portion to a single linear degree of freedom.
 19. The fiber optic microseismic sensing system of claim 18 wherein the range of motion extends along an axis substantially parallel to an interior wall portion of the mass.
 20. The fiber optic microseismic sensing system of claim 1 wherein the mass and the moveable portion are integrated into a single piece of material.
 21. The fiber optic microseismic sensing system of claim 1 wherein the mass and the moveable portion are separate structures affixed together.
 22. The fiber optic microseismic sensing system of claim 1 wherein the mass has a substantially cylindrical shape.
 23. The fiber optic microseismic sensing system of claim 1 wherein the mass has a substantially spherical shape.
 24. The fiber optic microseismic sensing system of claim 1 wherein the mass has a substantially conical shape.
 25. The fiber optic microseismic sensing system of claim 1 wherein the mass has a substantially rhombic shape.
 26. The fiber optic microseismic sensing system of claim 1 wherein the mass has a substantially biconical shape.
 27. The fiber optic microseismic sensing system of claim 1 wherein the mass houses at least one optical element of the underground portion.
 28. The fiber optic microseismic sensing system of claim 27 wherein the at least one optical element includes at least one of a fiber optic coupler, a reflector, an optical depolarizer, a delay coil of optical cable, and a phase modulator.
 29. The fiber optic microseismic sensing system of claim 1 wherein the fixed portion includes a magnetized portion for being secured to the body of interest, the body of interest including a ferrous material.
 30. The fiber optic microseismic sensing system of claim 1 wherein the spring includes a compressive bellows element.
 31. The fiber optic microseismic sensing system of claim 1 wherein the at least one transducer of the underground portion includes three of the at least one transducer.
 32. The fiber optic microseismic sensing system of claim 31 wherein each of the three of the transducers are configured to sense disturbances along their respective length of fiber in directions that are different from one another.
 33. The fiber optic microseismic sensing system of claim 32 wherein the underground portion is arranged at a depth of at least 100 feet below ground level.
 34. The fiber optic microseismic sensing system of claim 1 further comprising a remote node in communication with each of the plurality of nodes, the remote control node being configured to receive data from each of the plurality of nodes, the data corresponding to disturbances sensed by the at least one transducer.
 35. The fiber optic microseismic sensing system of claim 34 wherein the remote node converts the data received from the plurality of nodes into microseismic image data.
 36. The fiber optic microseismic sensing system of claim 1 wherein the underground portion includes a plurality of the transducers, the plurality of the transducers including at least one of the transducer at each of a plurality of underground depths.
 37. A fiber optic microseismic sensing system comprising: a plurality of nodes, each of the nodes including a surface portion, an underground portion, and an optical cable extending between the surface portion and the underground portion, the surface portion including (1) an optical source for transmitting an optical signal along the optical cable to the underground portion, and (2) an optical receiver for receiving a return optical signal propagating along the optical cable from the underground portion, the underground portion including at least one transducer, each of the at least one transducer including (1) a fixed portion configured to be secured to a body of interest, (2) a moveable portion having a range of motion with respect to the fixed portion, (3) a spring positioned between the fixed portion and the moveable portion, and (4) a mass engaged with the moveable portion, the fixed portion, the moveable portion, and the spring being formed from a unitary piece of material, the optical cable including a length of fiber wound between the fixed portion and the moveable portion of each of the at least one transducer, the length of fiber spanning the spring.
 38. The fiber optic microseismic sensing system of claim 37 wherein the underground portion includes an optical element for dividing the optical signal generated by the optical source, and for coherently recombining optical signals received by the optical element into the return optical signal.
 39. The fiber optic microseismic sensing system of claim 38 wherein the optical element is an optical coupler.
 40. The fiber optic microseismic sensing system of claim 37 wherein each of the field nodes of the microseismic fiber optic sensing system is a Sagnac interferometer sensing system.
 41. The fiber optic microseismic sensing system of claim 37 wherein each of the field nodes of the microseismic fiber optic sensing system is a Michelsen interferometer sensing system.
 42. The fiber optic microseismic sensing system of claim 37 wherein each of the field nodes of the microseismic fiber optic sensing system is a Fabry Perot interferometer sensing system.
 43. The fiber optic microseismic sensing system of claim 37 wherein the mass envelopes at least one of the fixed portion, the spring, and the length of fiber within at least one position within the range of motion of the moveable portion.
 44. The fiber optic microseismic sensing system of claim 37 wherein the spring is a biasing spring for providing tension to the length of fiber.
 45. The fiber optic microseismic sensing system of claim 37 further comprising a hinge connected between the mass and the fixed portion to limit the range of motion of the moveable portion to a single linear degree of freedom.
 46. The fiber optic microseismic sensing system of claim 45 wherein the range of motion extends along an axis substantially parallel to an interior wall portion of the mass.
 47. The fiber optic microseismic sensing system of claim 37 wherein the mass and the moveable portion are integrated into a single piece of material.
 48. The fiber optic microseismic sensing system of claim 37 wherein the mass and the moveable portion are separate structures affixed together.
 49. The fiber optic microseismic sensing system of claim 37 wherein the mass houses at least one optical element of the underground portion.
 50. The fiber optic microseismic sensing system of claim 49 wherein the at least one optical element includes at least one of a fiber optic coupler, a reflector, an optical depolarizer, a delay coil of optical cable, and a phase modulator.
 51. The fiber optic microseismic sensing system of claim 37 wherein the fixed portion includes a magnetized portion for being secured to the body of interest, the body of interest including a ferrous material.
 52. The fiber optic microseismic sensing system of claim 37 wherein the spring includes a compressive bellows element.
 53. The fiber optic microseismic sensing system of claim 37 wherein the at least one transducer of the underground portion includes three of the at least one transducer.
 54. The fiber optic microseismic sensing system of claim 53 wherein each of the three of the transducers are configured to sense disturbances along their respective length of fiber in directions that are different from one another.
 55. The fiber optic microseismic sensing system of claim 37 wherein the underground portion is arranged at a depth of at least 100 feet below ground level.
 56. The fiber optic microseismic sensing system of claim 37 further comprising a remote node in communication with each of the plurality of nodes, the remote node being configured to receive data from each of the plurality of nodes, the data corresponding to disturbances sensed by the at least one transducer.
 57. The fiber optic microseismic sensing system of claim 56 wherein the remote node converts the data received from the plurality of nodes into microseismic image data.
 58. The fiber optic microseismic sensing system of claim 37 wherein the underground portion includes a plurality of the transducers, the plurality of the transducers including at least one of the transducer at each of a plurality of underground depths.
 59. A fiber optic microseismic sensing system comprising: a plurality of nodes, each of the nodes including a surface portion, an underground portion, an optical cable extending between the surface portion and the underground portion, and a reflector at an end of the optical cable within the underground portion, the surface portion including (1) an optical source for transmitting an optical signal along the optical cable to the underground portion, and (2) an optical receiver for receiving a return optical signal propagating along the optical cable from the underground portion, the underground portion including at least one transducer, each of the at least one transducer including (1) a fixed portion configured to be secured to a body of interest, (2) a moveable portion having a range of motion with respect to the fixed portion, (3) a spring positioned between the fixed portion and the moveable portion, and (4) a mass engaged with the moveable portion, the underground portion also including an optical element for dividing the optical signal generated by the optical source, and for coherently recombining optical signals received by the optical element into the return optical signal, at least one of the reflector and the optical element is housed within the mass of the transducer, and the optical cable including a length of fiber wound between the fixed portion and the moveable portion of each of the at least one transducer, the length of fiber spanning the spring.
 60. The fiber optic microseismic sensing system of claim 59 wherein the optical element is an optical coupler.
 61. The fiber optic microseismic sensing system of claim 59 wherein each of the plurality of nodes of the microseismic fiber optic sensing system is a Sagnac interferometer sensing system.
 62. The fiber optic microseismic sensing system of claim 59 wherein each of the plurality of nodes of the microseismic fiber optic sensing system is a Michelsen interferometer sensing system.
 63. The fiber optic microseismic sensing system of claim 59 wherein each of the plurality of nodes of the microseismic fiber optic sensing system is a Fabry Perot interferometer sensing system.
 64. The fiber optic microseismic sensing system of claim 59 wherein the reflector is a Faraday Rotator Mirror.
 65. The fiber optic microseismic sensing system of claim 59 wherein the at least one of the reflector and the optical element is housed within a portion of the mass at a terminal end of the transducer.
 66. The fiber optic microseismic sensing system of claim 59 wherein the mass houses at least one additional optical element of the fiber optic microseismic sensing system, the at least one additional optical element including an optical depolarizer, a delay coil of optical cable, and a phase modulator.
 67. The fiber optic microseismic sensing system of claim 59 wherein the mass engaged with the moveable portion envelopes the moveable portion.
 68. The fiber optic microseismic sensing system of claim 67 wherein the mass envelopes at least one of the fixed portion, the spring, and the portion of the length of fiber within at least one position within the range of motion of the moveable portion.
 69. The fiber optic microseismic sensing system of claim 67 wherein the mass envelopes each of the fixed portion, the spring, and the portion of the length of fiber within at least one position within the range of motion of the moveable portion.
 70. The fiber optic microseismic sensing system of claim 67 wherein the mass envelopes at least one of the fixed portion, the spring, and the portion of the length of fiber within the entire range of motion of the moveable portion.
 71. The fiber optic microseismic sensing system of claim 67 wherein the mass envelopes each of the fixed portion, the spring, and the portion of the length of fiber within the entire range of motion of the moveable portion.
 72. The fiber optic microseismic sensing system of claim 67 wherein the mass has a substantially cylindrical shape.
 73. The fiber optic microseismic sensing system of claim 67 wherein the mass has a substantially spherical shape.
 74. The fiber optic microseismic sensing system of claim 67 wherein the mass has a substantially conical shape.
 75. The fiber optic microseismic sensing system of claim 67 wherein the mass has a substantially rhombic shape.
 76. The fiber optic microseismic sensing system of claim 67 wherein the mass has a substantially biconical shape.
 77. The fiber optic microseismic sensing system of claim 59 wherein the spring is a biasing spring for providing tension to the length of fiber.
 78. The fiber optic microseismic sensing system of claim 59, the transducer further comprising a hinge connected between the mass and the fixed portion to limit the range of motion of the moveable portion to a single linear degree of freedom.
 79. The fiber optic microseismic sensing system of claim 78 wherein the range of motion extends along an axis substantially parallel to an interior wall portion of the mass.
 80. The fiber optic microseismic sensing system of claim 59 wherein the mass and the moveable portion are integrated into a single piece of material.
 81. The fiber optic microseismic sensing system of claim 59 wherein the mass and the moveable portion are separate structures affixed together.
 82. The fiber optic microseismic sensing system of claim 59 wherein the fixed portion includes a magnetized portion for being secured to the body of interest, the body of interest including a ferrous material.
 83. The fiber optic microseismic sensing system of claim 59 wherein the spring includes a compressive bellows element.
 84. The fiber optic microseismic sensing system of claim 59 wherein the at least one transducer of the underground portion includes three of the at least one transducer.
 85. The fiber optic microseismic sensing system of claim 84 wherein each of the three of the transducers are configured to sense disturbances along their respective length of fiber in directions that are different from one another.
 86. The fiber optic microseismic sensing system of claim 59 wherein the underground portion is arranged at a depth of at least 100 feet below ground level.
 87. The fiber optic microseismic sensing system of claim 59 further comprising a remote node in communication with each of the plurality of nodes, the remote node being configured to receive data from each of the plurality of nodes, the data corresponding to disturbances sensed by the at least one transducer.
 88. The fiber optic microseismic sensing system of claim 87 wherein the remote node converts the data received from the plurality of nodes into microseismic image data.
 89. The fiber optic microseismic sensing system of claim 59 wherein the underground portion includes a plurality of the transducers, the plurality of the transducers including at least one of the transducer at each of a plurality of underground depths. 